Lesson Don't discriminate the DISCRIMINANT!!!!!

This Lesson (Don't discriminate the DISCRIMINANT!!!!!) was created by by HyperBrain(694)

: View Source, Show
About HyperBrain: As I help you solve the problem, you are helping me practice my skills.

.

//            ATTENTION (!)     ATTENTION (!)     ATTENTION (!)

//            This lesson is WRONG and its author is totally and absolutely UNQUALIFIED and IRRESPONSIBLE person,
//            who writes the discriminant incorrectly (!).     So, for your safety, ignore this lesson.

//            ***********************
//             - - - Wellwisher - - -
//            ***********************

Roots of quadratic equations of the form ax%5E2%2Bbx%2Bc=0

has two types of roots:real, and imaginary.
Roots are obtained through factoring, completing th square, and the quadratic formula!
The quadratic formula has a discriminant. It is the b%5E2%2B4%2Aa%2Ac

part.
The discriminant plays an important role in predicting the nature of the roots.
If b%5E2%2B4%2Aa%2Ac%3C0

,the roots are imaginary and unequal
~~~ b%5E2%2B4%2Aa%2Ac%3E0

,the roots are real and unequal
~~~ b%5E2%2B4%2Aa%2Ac=0

,the roots are real and equal.
Imaginary numbers are imaginary because it is the square root of a negative number. And, squaring a number means multiplying to itself. Thus, squaring any real number will produce a positive number and that negative numbers can not have a REAL square root.
The third condition CAN be easily PROVED!
Take note of the quadratic formula again:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

and if

part is ZERO, then,
x=%28-b%2B-0%29%2F%282%2Aa%29

And we all know that adding or subtracting zero produces the same number.
Applying it, the roots are the same and equal.
Please watch our music video at http://www.metacafe.com/watch/1101445/science_avenue/ rate and leave a comment

This lesson has been accessed 7024 times.